Solving a system of equations
We want to find where x and y are equal in both equations.
First step: replacing the x value given by the second equation in the first
3x + 4y = 8
x = 16 - 4y
↓
3(16 - 4y) + 4y = 8
Distributing the parenthesis:
3 · 16 - 3 · 4y + 4y = 8
48 - 12y + 4y = 8
48 - 8y = 8
Rearranging the equation:
48 - 8y = 8
48 - 8 = 8y
40 = 8y
40/8 = y
5 = y
Second step: replacing the 5 = y value in one of the equations
We replace it in the second equation:
x = 16 - 4y
x = 16 - 4 · 5
x = 16 - 20
x = -4
Solution: y = 5 amd x = -4